HARD
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Important Questions on Number Theory

EASY

The sum of three consecutive numbers is 126. Find the highest number-

1. 41
2. 42
3. 43
4. 44

HARD
The number of all 2-digit numbers n such that n is equal to the sum of the square of digit in its tens place and the cube of the digit in units place is
EASY

How many times does the number 3 occur in unit's place for numbers ranging from 1 to 100?

1. 20
2. 11
3. 10
4. 19

MEDIUM
If 59 is added to a square of a number, the result is 900. What is the number?
MEDIUM
There are exactly twelve Sundays in the period from January 1 to March 31 in a certain year. Then, the day corresponding to February 15 in that year is
EASY

1 USD = Rs. 67.89. A money changer adds a margin of Rs. 1.11. What will be the cost of 150 USD ? 

1. Rs. 10,183
2. Rs. 10,350
3. Rs. 10,330
4. Rs. 10,450

MEDIUM
The number of digits in the decimal expansion of 165516 is
MEDIUM
The least number, which is to be added to the greatest number of 4 digits so that the sum may be divisible by 345, is _____.
MEDIUM
Consider the set A of natural numbers n whose units digit is non-zero, such that if this units digit is erased, then the resulting number divides n. If K is the number of elements in the set A, then
MEDIUM

Consider a three-digit number with the following properties:

I. If its digits in units place and tens place are interchanged, the number increases by 36
II. If its digits in units place and hundreds place are interchanged, the number decreases by 198 .

Now, suppose that the digits in tens place and hundreds place are interchanged. Then, the number

EASY
The difference of the cubes of two consecutive numbers is 127. What are the numbers?
HARD
Let a, b, c be three distinct positive integers such that the sum of any two of them is a perfect square and having minimal sum a+b+c. Find this sum.
EASY
If 14 of third-part of number is 5, then the number is:
EASY

Twice the difference between two numbers is equal to their sum. If one number is 15, Find the other number.

1. 15
2. 10
3. 5
4. 20 

EASY
The sum of two digits of a number is 13. If 9 is subtracted from the number, the digits are interchanged. What is the number?
EASY
1800 chocolates were distributed among the students of a class. Each student got twice as many chocolates as the number of students in the class. Calculate the number of students in the class.
EASY
Find the unit place digit in (82)102+(183)103
MEDIUM
The number of positive integers n in the set 2,3,..,200 such that 1n has a terminating decimal expansion is
HARD
Let S be the set of all point ab,cd on the circle with radius 1 centred at 0,0 where a and b are relatively prime integers, c and d are relatively prime integers (that is HCF a,b=HCF c,d=1), and the integers b and d are even. Then the set S
HARD
Determine the number of 8 -tuples ϵ1,ϵ2,.ϵ8 such that ϵ1,ϵ2,ϵ3,.ϵ8-1,1 and ϵ1+2ϵ2+3ϵ3+..+8ϵ8 is a multiple of 3.